This is just the southern half of the route. It is very long route stretching from Piazza Risorgimento north of the Vatican all the way to end south and east of Termini.
Frome Circo Maximo 81 bus turns down Via di Gregorio and reaches the Colosseum by Celio Vibenna. The route turns south on Via Claudia and tghen truns on Via dell'Ambra Aradam. It runs down to San Giovanni Laterno. The 81 route continues on down Via La Spezia before reaching it's terminus.

The brown line shows the diffenrt way that Route 81 returns to the Vatican end when moving north and westward.